In this paper the Extended Ornstein-Uhlenbeck process (EOU) and the Fat-tailed and Correlated Stochastic Volatility process (FCSV) are used in Bayesian pricing of European call options. The main difference between EOU and FCSV models is that the first of them is a continuous process whilst the second one is a discrete process. The Bayesian option pricing is based on the distribution of the payoff function given by the predictive density of future observables. The basic instrument was WIG20 index. The most surprising conclusion of our research is a similarity of forecast and option pricing based on different Bayesian models. The results presented in the paper are obtained by Monte Carlo Markov chain. The Metropolis-Hastings algorithm and the acceptance-rejection sampling are used within the Gibbs sampler. (original abstract)